Coion concentration in the

In Equation 15.47, the contact layer is positioned at the surface, i.e., x=0, i.e., c,(0)=c,. We now make the following assumptions first, the electrostatic repulsion is so strong that the coion concentration in the contact layer is zero, i.e., Ca=0, second, the accumulation of counterion is so high that Cbi is much higher than and Equation 15.47 is approximated to... 

First we consider the electrostatic (double layer) interaction between two identical charged plane parallel surfaces across a solution of symmetric Z Z electrolyte. The charge of a counterion (i.e., ion with charge opposite to that of the surface) is -Ze, whereas the charge of a coion is +Ze (Z = +1, +2,. ..) with e the elementary charge. If the separation between the two planes is very large, the number concentration of both counterions and coions would be equal to its bulk value, n, in the middle of the film. However, at finite separation, h, between the surfaces the two EDL overlap and the counterion and coion concentrations in the middle of the film, io and 2o> longer equal. Because the solution inside the film is supposed to be in electrochemical (Donnan) equilibrium with the bulk electrolyte solution of concentration q, we can write 20 0 or, alternatively,... 

Fig. 15. Cluster network model for highly cation-permselective Nafion membranes126). Counterions are largely concentrated in the high-charge shaded regions which provide somewhat tortuous, but continuous (low activation energy), diffusion pathways. Coions are largely confined to the central cluster regions and must, therefore, overcome a high electrical barrier, in order to diffuse from one cluster to the next...

Due to the electrostatic repulsion the coion concentration inside the diffuse part of the DL is decreased, which is the reason for the relatively low concentration of coions in the sublayer compared with the concentration at the boundary between the diffuse and difffision layer, i.e. at X = k". ... 

In experiments at trace level or very low loading of one ion, the isotope dilution procedure is not required. All that is necessary is that the exchangeable ions on the solid be those of the salt present in macro concentration. The computation of results, which followed that conventionally used in the determination of distribution coefficients, ignores possible effects of colon exclusion from water in the clay pack it is implicitly assumed that the water in the pack has the same coion concentration as the supernatant solution. It is possible that coion exclusion has an effect which may be significant on distribution coefficients (particularly when they are low) and on capacities computed from the results. We shall discuss this interference later in connection with the capacities measured by displacement of both cations and anions from the clay pack and associated water. Coion exclusion has been further discussed in references 1 and 7 (see also 8, 9, and 10). 

In the theoretical approaches of Poisson-Boltzmann, modified Gouy-Chapman (MGC), and integral equation theories such as HNC/MSA, concentration or density profiles of counterions and coions are calculated with consideration of the ion-waU and ion-ion in-... 

FIG. 5 Normalized concentration distribution in the pore of Figure 4 but charged with —0.05 C/m. The symbols are the same as in Figure 4, with the cations being the counterions. The anions (coions) of the RPM and SPM model are not distinguishable on the present scale. The dotted line is the prediction of the modified Gouy-Chapman theory and approximates the simulation results of the RPM. 

RPM model, but theories for the SPM model electrolyte inside a nanopore have not been reported. It is noticed that everywhere in the pore, the concentration of counterion is higher than the bulk concentration, also predicted by the PB solution. However, neutrality is assumed in the PB solution but is violated in the single-ion GCMC simulation, since the simulation result of the counterion in the RPM model is everywhere below the PB result. There is exclusion of coion, for its concentration is below the bulk value throughout the pore. Only the solvent profile in the SPM model has the bulk value in the center of the pore. 

One attraction of MD simulation is the possibility of computer animation. The mobility of ions inside a charged cylindrical pore can be visualized. Some movie clips of EMD and NEMD are downloadable at http //chem.hku.hk/ kyc/movies/. mpg. Some features that escape statistical averages can be learned in watching the animation. While the coions are present mainly in the center of the pore, occasional collisions with the wall do occur, as observed in the movie. The time scale of a coion staying near the wall is of the order of 1 ps, compared to 10 ps for the counterion. While the averaged equilibrium distributions indicate an infinitesimal concentration of coion at the wall, reaction of coion with the wall can occur within a time scale of 1 ps. From the video, it can also be observed that the radial mobility of the counterion is more significant compared to the coion s and compared to the axial mobility. It is consistent with the statistical results. 

The positive-positive particles will show repulsion. On the other hand, the positive-negative particles will attract each other. The ion distribution will also depend on the concentration of any counterions or coions in the solution. Even glass, when dipped in water, exchanges ions with its surroundings. Such phenomena can be easily investigated by measuring the change in the conductivity of the water. 

E> can be measured directly by membrane or vapor pressure osmometry. The application of an alternative method was described recently [64, 65]. It is based on an analysis of the sedimentation equilibrium in an analytical ul-tracentrifuge, where the solution contains the polyelectrolyte as well as a small concentration of an inert salt. In sedimentation equilibrium, the concentration gradients of both components are coupled via a Donnan-type equilibrium, which is governed by the effective charge number zeff of the polyion. Both concentration gradients can be determined in one experiment, when the polyion and the coion of the salt have sufficiently separated absorption bands in the UV or visible range. 

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